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April, 2019 The logarithmic derivative for point processes with equivalent Palm measures
Alexander I. BUFETOV, Andrey V. DYMOV, Hirofumi OSADA
J. Math. Soc. Japan 71(2): 451-469 (April, 2019). DOI: 10.2969/jmsj/78397839

Abstract

The logarithmic derivative of a point process plays a key rôle in the general approach, due to the third author, to constructing diffusions preserving a given point process. In this paper we explicitly compute the logarithmic derivative for determinantal processes on $\mathbb{R}$ with integrable kernels, a large class that includes all the classical processes of random matrix theory as well as processes associated with de Branges spaces. The argument uses the quasi-invariance of our processes established by the first author.

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Alexander I. BUFETOV. Andrey V. DYMOV. Hirofumi OSADA. "The logarithmic derivative for point processes with equivalent Palm measures." J. Math. Soc. Japan 71 (2) 451 - 469, April, 2019. https://doi.org/10.2969/jmsj/78397839

Information

Received: 6 July 2017; Revised: 17 October 2017; Published: April, 2019
First available in Project Euclid: 4 March 2019

zbMATH: 07090051
MathSciNet: MR3943446
Digital Object Identifier: 10.2969/jmsj/78397839

Subjects:
Primary: 60G55
Secondary: 60J60

Keywords: Determinantal processes , infinite-dimensional diffusion , logarithmic derivative , Palm measure , Point processes

Rights: Copyright © 2019 Mathematical Society of Japan

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Vol.71 • No. 2 • April, 2019
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